Flying toys which are thrown by a user and rotate to effect an aerodynamically optimised flight are widely used and come in a wide variety of forms, from ring structures such as the Aerobie to the Frisbee. Disc Golf is an increasingly popular sport and the flying discs used to play it are regulated by the PDGA (Professional Disc Golf Association) and manufacturers include Ching, Disc Golf Association, Discraft Inc., Disc Golf Stuff, Dynamic Discs, Gateway Disc Sports, Innova-Champion Discs Inc., Lightning Discs, Millennium Golf Discs, Superflight Inc., and Wham-O.
A typical disc is axially symmetric with an upper surface plate of minimum thickness adjoined to (i.e. contiguous with) a rim of carefully designed depth. In modem flying discs, the mass of the disc is removed to the rim to maximise the angular momentum given to the disc at launch and subsequently reduce the rate at which the disc rolls (and pitches) in flight. The rim and plate together define a cavity beneath the plate that, due to the high pressure difference caused by the trailing edge rim, stabilises the pitching moment and inhibits the gyroscopic roll rate to within acceptable bounds for free-flight.
Flying discs are aerodynamically unstable. However, the spin decouples the pitching moment from the pitch, leaving the angle of attack unaffected. This primarily results in a minimal roll rate (instead of pitch) and therefore the disc remains at a consistent orientation to the oncoming wind throughout each rotation. For a right-handed backhand throw, for example, the roll direction is typically port wing up at launch with transition to starboard wing up towards the end of the flight, generating the widely observed S-shaped flight trajectory. This S-shaped flight path is feasible provided that the disc flies through its zero pitching moment trim condition, i.e. at launch the typically nose down (negative) pitching moment provides roll, bank and curve in the opposite lateral direction to that exhibited late on in the flight when there is a nose up (positive) pitching moment, the initial lateral direction being dependent upon the spin vector.
The flying disc cross-sectional profile is an aerofoil or lifting surface, typically with symmetry about its mid-chord (center) (although some flying discs are made asymmetric, i.e. are not axi-symmetric, with the center of the cavity being offset from the center of the upper surface plate). Aerofoils comprising symmetric sections are uncommon in aeronautical applications when compared to conventional aerofoils which have an asymmetric cross-section comprising a blunt leading edge and sharp trailing edge. An axi-symmetric disc spins about its centroid, which is the location of the center of gravity. Axi-symmetry also provides a disc with consistent aerodynamic characteristics throughout each rotation, due to the consistent geometric orientation of the disc to the oncoming wind.
The aerodynamic performance of a flying disc is primarily dependent upon the lift, drag and pitching moment load characteristics.
Lift is generated by the difference in relative pressure below the wing surface compared with that above the wing surface. The aerodynamic pressure difference creates a lifting force to counteract the force due to gravity and thus retards the loss of altitude. For a flying disc, lift contributions come from the (relatively) large pressure differences found on the nose and tail. The pressure difference on the nose is driven by accelerated air passing over the upper nose surface, which generates a low pressure suction above the nose. The pressure difference on the tail is caused by the presence of the inside rim surface which sets up higher pressure below the tail.
Drag is generated by the force of the air on the disc in the direction opposite to that in which it travels. Primary contributions to the drag are the suction on the nose inside rim and the higher pressure on the tail inside rim. The lower rim surfaces create turbulence beneath the disc, which affects the downwash and induced drag.
Primary contributions to the pitching moment are due to the strength of the two (lifting) pressure differences on the nose and tail. The unbalanced strength of these lifting forces, forward and aft of the center, generate an untrimmed (i.e. non-zero) pitching moment. Nose up (positive) pitching moment occurs when the torque due to the lift on the nose is stronger than the torque due to the lift on the tail. Nose down (negative) pitching moment occurs when the torque due to the lift on the tail is stronger than the torque due to the lift on the nose.
The various manufacturers of golf (flying) discs aim to optimise a range of properties, including flight characteristics, ability to fly, and throwability. Various patents exist for flying discs and include U.S. Pat. Nos. 3,359,678, 4,568,297 and 6,179,737. Design patents also exist and include U.S. Pat. No. 402,318.
In U.S. Pat. No. 4,568,297, a one-piece flying disc is disclosed having a convex upper surface, an annular rim having an equilateral triangle cross-section with a straight lower edge between: (i) a lower rounded corner of the rim forming a lower edge; and (ii) an outer rounded corner. In particular, it seeks to increase the flight efficiency by reducing drag, increasing the lifting area, and redistributing mass towards the rim of the disc.
A wide range of flying discs are commercially available (above) incorporating the features of U.S. Pat. No. 4,568,297, and typically have a convex upper surface and a concave lower surface.
U.S. Pat. No. 6,179,737 discloses flying discs having an outer rim portion encompassing a thin central plate, and whose cross-section from the central plate to the top and bottom edges of the rim comprises concave curves (fillet curves).
Generally speaking, to improve the aerodynamic performance of a flying disc, the aim is to maximise lift, minimise drag and minimise the pitching moment gradient with angle of attack. The improvement of one out of three of these can often incur a performance penalty in one or more of the other two. Therefore, to improve overall aerodynamic performance the lift, drag and pitching moment combination is crucial. Improved performance can be achieved by creating stronger pressure differences (improved lift) particularly on the tail (increased nose down pitching moment) or by further streamlining (improved drag).